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Abstract: We analyse the density of states of the random graph Laplacian in thepercolating regime. A symmetry argument and knowledge of the density of statesin the nonpercolating regime allows us to isolate the density of states of thepercolating cluster DSPC alone, thereby eliminating trivially localisedstates due to finite subgraphs. We derive a nonlinear integral equation for theintegrated DSPC and solve it with a population dynamics algorithm. We discussthe possible existence of a mobility edge and give strong evidence for theexistence of discrete eigenvalues in the whole range of the spectrum.



Author: T. Aspelmeier, A. Zippelius

Source: https://arxiv.org/







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